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2. Prior to taking an aerobic lesson, each of the 12 health-club members is asked to rate the instructor on a scale of 3=exce
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Answer #1

H0 = There is no significant improvement in instructor's rating

H1 = There is a significant improvement in instructor's rating

Assume = 0,05

Decision Criterion:

Reject H0 if and only if Test Statistic > t11 @ \alpha = 0.05

i.e. if and only if Test Statistic > 1.796

Test Statistic = \frac{D^{*} - (\mu_{post} - \mu_{pre})}{\frac{S_{D}}{\sqrt{n}}}

where D* = Average of the differences between pre and post

i.e = D* = 0.75

SD = \frac{1}{n - 1} \times \sum_{1}^{n} D_{i}^{2} - nD^{*^{2}} = 0.866

where Di's are individual differences between pre and post

Therefore, test statistic = \frac{0.75 - (2.583 - 1.833)}{\frac{0.866}{\sqrt{12}}} = 0

Since test statistic = 0 is not grester than 1.796, we retain H0 and reject H1, i.e. post course ratings do not change at 5% level of significance

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